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Local and parallel finite element method for solving the biharmonic eigenvalue problem of plate vibration
Author(s) -
Zhao Ruilin,
Yang Yidu,
Bi Hai
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22329
Subject(s) - biharmonic equation , mathematics , eigenvalues and eigenvectors , finite element method , mathematical analysis , vibration , inverse iteration , divide and conquer eigenvalue algorithm , boundary value problem , physics , quantum mechanics , thermodynamics
In this paper, we establish a new local and parallel finite element discrete scheme based on the shifted‐inverse power method for solving the biharmonic eigenvalue problem of plate vibration. We prove the local error estimation of finite element solution for the biharmonic equation/eigenvalue problem and prove the error estimation of approximate solution obtained by the local and parallel scheme. When the diameters of three grids satisfy H 4 = ϑ( w 2 ) = ϑ( h ), the approximate solutions obtained by our schemes can achieve the asymptotically optimal accuracy. The numerical experiments show that the computational schemes proposed in this paper are effective to solve the biharmonic eigenvalue problem of plate vibration.